Glossary

A

Adiabatic invariant — A quantity that remains constant when a parameter of a system changes slowly. In plasma physics, the magnetic moment \(\\mu = m v_\\perp^2/(2B)\) is an adiabatic invariant for a particle gyrating in a slowly varying magnetic field. See Adiabatic Invariant.

Alfvén speed — The characteristic speed at which transverse MHD disturbances propagate along magnetic field lines: \(v_A = B/\\sqrt{\\mu_0 \\rho}\). See Alfvén Speed.

B

Boltzmann response — The relation \(n_{e1}/n_0 = e\\phi_1/(k_B T_e)\) describing how electrons redistribute in response to a small electrostatic potential.

Bohm criterion — The condition \(v_i \\ge c_s\) at the sheath edge, required for a stable plasma–wall transition. See Plasma Sheath.

Buneman instability — A two-stream instability that occurs when the electron drift speed exceeds the ion thermal speed. See Streaming Instability.

C

Collective parameter — \(\\Lambda = 4\\pi n \\lambda_D^3\), the average number of electrons inside a Debye sphere. \(\\Lambda \\gg 1\) defines an ideal plasma.

Continuity equation — \(\\partial \\rho/\\partial t + \\nabla\\cdot(\\rho \\mathbf{U}) = 0\), expressing mass/particle conservation. See Continuity Equation.

Cold plasma — A plasma model where finite temperature effects are neglected; only fluid motion and fields are retained.

D

Debye length — The screening length in a plasma: \(\\lambda_D = \\sqrt{\\varepsilon_0 k_B T_e / (n_e e^2)}\). See Debye Length.

Drift motion — Particle motion perpendicular to \(\\mathbf{B}\) caused by inhomogeneities or forces: \(\\mathbf{E}\\times\\mathbf{B}\) drift, grad-B drift, curvature drift. See Drift Motion.

E

Equation of state — Relation between pressure and density. For isothermal electrons: \(p_e = n_e k_B T_e\); for adiabatic ions: \(p_i \\propto n_i^{\\gamma_i}\).

F

Frozen-in theorem — In ideal MHD (\(\\eta = 0\)), magnetic field lines are “frozen” into the plasma and move with the fluid velocity \(\\mathbf{U}\). See Frozen-in Theorem.

G

Grad–Shafranov equation — The fundamental PDE of axisymmetric MHD equilibrium: \(\\Delta^*\\psi + \\mu_0 R^2 dp/d\\psi + F dF/d\\psi = 0\). See Grad–Shafranov Equation.

I

Ideal plasma — A plasma satisfying \(\\lambda_D \\ll L\), \(\\Lambda \\gg 1\), and quasi-neutrality. See Ideal Plasma.

Induction equation — \(\\partial \\mathbf{B}/\\partial t = \\nabla\\times(\\mathbf{U}\\times\\mathbf{B}) + \\eta\\nabla^2\\mathbf{B}\), describing magnetic field evolution in MHD. See Induction Equation.

Ion acoustic wave — A low-frequency electrostatic wave with dispersion \(\\omega^2 = k^2 c_s^2/(1 + k^2\\lambda_{De}^2)\). See Ion Acoustic Wave.

L

Landau damping — Collisionless damping of plasma waves due to resonant wave–particle interaction, governed by \(\\partial f_0/\\partial v\) at \(v = \\omega/k\). See Landau Damping.

Langmuir waves — High-frequency electrostatic electron oscillations with dispersion \(\\omega^2 = \\omega_{pe}^2 + 3k^2 v_{te}^2\). See Langmuir Waves.

Larmor radius — The gyroradius of a charged particle in a magnetic field: \(\\rho_s = m_s v_{\\perp}/(|q_s| B)\). See Larmor Radius.

Loss cone — The range of pitch angles for which particles can escape a magnetic mirror. Particles with \(\\sin^2\\theta < B_{\\text{min}}/B_{\\text{max}}\) are lost. See Magnetic Mirror.

Lundquist number — The magnetic Reynolds number in MHD: \(S = \\mu_0 v_A L/\\eta\). See Lundquist Number.

M

Magnetic island — A closed flux region formed during magnetic reconnection, bounded by separatrices. See Magnetic Islands.

Magnetic mirror — A magnetic configuration where increasing field strength reflects charged particles, trapping them between two high-field regions. See Magnetic Mirror.

Magnetohydrodynamics (MHD) — Fluid description of a plasma as a single conducting fluid coupled to electromagnetic fields. See MHD.

Magnetized wave — Electromagnetic wave in a magnetized plasma, classified as R, L, O, or X mode. See Magnetized Waves.

P

Plasma — An ionized gas in which collective electromagnetic effects dominate over binary collisions. See Plasma.

Plasma approximation — The condition \(\\lambda_D \\ll L\) that allows a plasma to be treated as a continuous medium.

Plasma frequency — The natural electron oscillation frequency: \(\\omega_{pe} = \\sqrt{n_e e^2/(m_e \\varepsilon_0)}\). See Plasma Frequency.

Plasma parameter — \(\\Lambda = 4\\pi n \\lambda_D^3\); measures the number of particles in a Debye sphere.

Plasma wave — Collective oscillation of a plasma: Langmuir, ion acoustic, Alfvén, magnetosonic, etc. See Plasma Waves.

Poisson’s equation — \(\\nabla^2 \\phi = -\\rho/\\varepsilon_0\); relates charge density to electrostatic potential. See Poisson’s Equation.

Q

Quasi-neutrality — The condition \(|n_e - Z n_i| \\ll n_e\) on macroscopic scales \(L \\gg \\lambda_D\). See Quasi-neutrality.

S

Sound speed — The characteristic speed of pressure propagation in a plasma: \(c_s = \\sqrt{(\\gamma_e k_B T_e + \\gamma_i k_B T_i)/m_i}\). See Sound Speed.

Sweet–Parker model — A steady-state MHD reconnection model predicting \(M_A \\sim S^{-1/2}\) for a long thin current sheet. See Sweet–Parker Model.

V

Vlasov equation — The collisionless Boltzmann equation for the phase-space distribution function \(f(\\mathbf{r}, \\mathbf{v}, t)\). See Vlasov Equation.

W

Waves in plasmas — See Plasma Waves and Magnetized Waves.